Optical method and system for extended depth of focus

ABSTRACT

An imaging arrangement and method for extended the depth of focus are provided. The imaging arrangement comprises an imaging lens having a certain affective aperture, and an optical element associated with said imaging lens. The optical element is configured as a phase-affecting, non-diffractive optical element defining a spatially low frequency phase transition. The optical element and the imaging lens define a predetermined pattern formed by spaced-apart substantially optically transparent features of different optical properties. Position of at least one phase transition region of the optical element within the imaging lens plane is determined by at least a dimension of said affective aperture.

FIELD OF THE INVENTION

This invention is generally in the field of imaging systems, and relatesto an imaging lens arrangement with increased depth of focus.

BACKGROUND OF THE INVENTION

Extending the depth of focus of imaging systems is a very important coretechnology allowing its incorporation into various applications,including inter alia medically related applications where elements, suchas cameras, are to be inserted into the body in order to observe anddetect problematic tissues; as well as ophthalmic industry includingglasses for spectacles, contact lenses, intraocular lenses or otherlenses inserted surgically into the eye. The extended depth of focussolution is also needed for optical devices like microscopes or camerasfor industrial, medical, surveillance or consumer applications, wherefocusing of light is required and where today focusing is beingimplemented by a multitude of lenses with the need of relativedisplacement between the focusing arrangement and an image and/or objectplane, by mechanical movement, either manually or electronically driven.

Various approaches have been developed for obtaining extended depth offocus of an optical system. One of the known approaches, developed bythe inventor of the present invention, is disclosed in WO 03/076984.This technique provides an all-optical extended depth of field imaging.An imaging system produces images of acceptable quality of objects whichare located at a wide variety of distances from the imaging system. Apreferred embodiment of the imaging system includes an object, anauxiliary lens, a composite phase mask and a sensor arranged along anoptical axis. Light from the object is focused by the auxiliary lens intandem with the composite phase mask, producing an image which isincident on the detector. This technique is based upon placing aspatially highly resolved phase element on top of the lens aperture suchthat continuous set of focal length is generated.

Another approach is disclosed for example in the following publications:U.S. Pat. No. 6,069,738; U.S. Pat. No. 6,097,856; WO 99/57599; WO03/052492. According to this approach, a cubic phase mask is used in theaperture plane, and digital post processing is required to realize afocused image. More specifically:

U.S. Pat. No. 6,069,738 discloses an apparatus and methods for extendingdepth of field in image projection systems. An optical system forproviding an in-focus, extended depth of field image on a projectionsurface includes an encoded mask or light encoder for preceding thelight to include object information (or, equivalently, information aboutthe desired image), and an extended depth of field (EDF) mask, forextending the depth of field of the projection system. In addition toincluding object information, the encoded mask encodes the light fromthe light source to account for the variations introduced by the EDFmask in extending the depth of field, so that no post processing isrequired.

U.S. Pat. No. 6,097,856 discloses an apparatus and method for reducingimaging errors in imaging systems having an extended depth of field. Animproved optoelectronic imaging system is adapted for use withincoherently illuminated objects, and which produces final images havingreduced imaging error content. The imaging system includes an opticalassembly for forming an intermediate image of the object to be imaged,an image sensor for receiving the intermediate image and producing anintermediate image signal, and processing means for processing theintermediate image signal to produce a final image signal having areduced imaging error content. A reduction in imaging error content isachieved, in part, by including in the optical assembly a phase mask forcausing the OTF of the optical assembly to be relatively invariant overa range of working distances, and an amplitude mask having atransmittance that decreases continuously as a function of distance fromthe center thereof. The reduction in imaging error content is alsoachieved, in part, by including in the processing means an improvedgeneralized recovery function that varies in accordance with at leastthe non-ideal calculated IOTF of the optical assembly under a conditionof approximately optimum focus.

WO 99/57599 discloses an optical system for increasing the depth offield and decreasing the wavelength sensitivity of an incoherent opticalsystem. The system incorporates a special purpose optical mask into theincoherent system. The optical mask has been designed to cause theoptical transfer function to remain essentially constant within somerange from the in-focus position. Signal processing of the resultingintermediate image undoes the optical transfer modifying effects of themask, resulting in an in-focus image over an increased depth of field.Generally the mask is placed at or near an aperture stop or image of theaperture stop of the optical system. Preferably, the mask modifies onlyphase and not amplitude of light, though amplitude may be changed byassociated filters or the like. The mask may be used to increase theuseful range of passive ranging systems.

WO 03/052492 discloses a technique providing extended depth of focus(EDF) to human eyes by modifying contact lenses, intraocular implants,or the surface of the eye itself. This is accomplished by applyingselected phase variations to the optical element in question (forexample, by varying surface thickness). The phase variations EDF-codethe wavefront and cause the optical transfer function to remainessentially constant within some range away from the in-focus position.This provides a coded image on the retina. The human brain decodes thiscoded image, resulting in an in-focus image over an increased depth offocus.

Yet other approaches, disclosed for example in U.S. Pat. No. 6,554,424(as well as U.S. patent application publications 20040114103;20040114102; and 20030142268) and U.S. Pat. No. 4,955,904, utilizeapodization of the aperture plane. More specifically:

U.S. Pat. No. 6,554,424 describes a system and method for increasing thedepth of focus of the human eye. The system is comprised of a lens body,an optic in the lens body configured to produce light interference, anda pinhole-like optical aperture substantially in the center of theoptic. The optic may be configured to produce light scattering orcomposed of a light reflective material. Alternatively, the optic mayincrease the depth of focus via a combination of light interference,light scattering, light reflection and/or light absorption. The opticmay also be configured as a series of concentric circles, a weave, apattern of particles, or a pattern of curvatures. One method involvesscreening a patient for an ophthalmic lens using a pinhole screeningdevice in the lens to increase the patient's depth of focus. Anothermethod comprises surgically implanting a mask in the patient's eye toincrease the depth of focus.

U.S. Pat. No. 4,955,904 describes a masked intraocular lens forimplantation into a human eye. The mask, which blocks only part of thelens body, together with the pupil of the eye, defines a small aperturein the eye when the pupil is constricted, thereby increasing the depthof focus, as a pinhole camera does. When the pupil of the eye isdilated, additional light is allowed to pass through the pupil aroundthe mask and to reach the retina to allow a person to see in dimmerlight conditions. In one embodiment, the mask defines a small circularaperture and a larger exterior annulus; the small circular aperture hasan additional power intermediate between that needed for distance andclose vision. Also provided is a method for treating a patient withcataracts comprising replacing the patient's lens with this maskedintraocular lens.

Some other vision improvement techniques are disclosed in the followingpatent publications:

U.S. Pat. No. 5,748,371 discloses extended depth of field opticalsystems. The system for increasing the depth of field and decreasing thewavelength sensitivity and the effects of misfocus-producing aberrationsof the lens of an incoherent optical system incorporates a specialpurpose optical mask into the incoherent system. The optical mask hasbeen designed to cause the optical transfer function to remainessentially constant within some range from the in-focus position.Signal processing of the resulting intermediate image undoes the opticaltransfer modifying effects of the mask, resulting in an in-focus imageover an increased depth of field. Generally the mask is placed at aprincipal plane or the image of a principal plane of the optical system.Preferably, the mask modifies only phase and not amplitude of light. Themask may be used to increase the useful range of passive rangingsystems.

WO 01/35880 discloses multifocal aspheric lens, an optical surface inclose proximity to a person's pupil for correcting presbyopia, a methodfor obtaining that optical surface, and a laser surgery system to carryout the method. The optical surface includes a first vision area, asecond vision area surrounding the first area, and a third vision areasurrounding the second vision area, the first vision area having a firstsubstantially single power, the second vision area having a range ofpowers, the third vision area having a second substantially single powerdistinct from the first single power, at least one of the first, secondand third vision areas having an aspheric surface, and the other areashaving spherical surfaces. The method includes reshaping the cornea toobtain this optical surface. The cornea may be reshaped on the anterioror an underlying surface by ablation or collagen shrinkage, wherein theablation is performed by applying an excimer laser, surgical laser,water cutting, fluid cutting, liquid cutting or gas cutting technique.The method also includes obtaining this optical surface by placing acontact lens having the desired optical characteristics on the cornea.The laser surgery system includes a laser beam generator and a laserbeam controller to regulate the beam striking the cornea to remove aselected volume of corneal tissue from a region in an optical zone ofthe cornea with the ablative radiation, thereby forming a reprofiledregion which has a first vision area, a second vision area surroundingthe first area, and a third vision area surrounding the second visionarea.

U.S. Pat. No. 5,965,330 discloses methods for fabricating annular masklens having diffraction-reducing edges. According to this technique, thelens body has an annular mask that forms a “soft edge” by graduallydecreasing the transmissivity radially from the center aperture to theannular mask area. The methods introduce varying levels of a coloringagent (e.g., dye) into certain portions of the lens.

WO 03/012528 describes an apparatus for generating a light beam with anextended depth of focus. The apparatus includes a binary phase mask thatgenerates a diffraction pattern including bright main ring and twoside-lobe rings, an annular aperture mask that passes only part of thediffraction pattern, and a lens that causes the light passing throughthe annular aperture to converge towards and cross the optical axis.Where the converging light crosses the optical axis, constructiveinterference takes place, generating a light beam that has an extendeddepth of focus.

U.S. Pat. Nos. 5,786,883; 5,245,367 and 5,757,458 describe an annularmask contact lens designed to operate with the normal functioning of thehuman pupil. An annular mask forms a small pinhole-like aperture on thecontact lens enabling continual focus correction. The outer diameter ofthe annular mask allows the wearer to transmit more light energy throughthe pupil as brightness levels decrease. The contact lens may bestructured with two separate and distinct optical corrections, both atthe small aperture region and in the region beyond the annular mask.Functional imaging is thus achieved for both bright and dim lighting,and over a wide range of viewing distances.

U.S. Pat. No. 5,260,727 discloses wide depth of focus intraocular andcontact lenses. According to this technique, the lens power can be aconstant but the amplitude and phase of the wave across the pupillaryaperture are variables. The lens can be constructed by shading regionsthereof in accordance with a mathematical function, e.g., a Gaussiandistribution or Bessel function over a predetermined geometry, such ase.g., concentric, parallel or radial. The lens may be of single power ormultiple power, e.g., of the bi-focal type.

U.S. Pat. No. 5,905,561 discloses an annular mask lens for visioncorrection having diffraction reducing edges. The lens body has anannular mask that forms a “soft edge” by gradually decreasing thetransmissivity radially from the center aperture to the annular maskarea.

U.S. Pat. No. 5,980,040 describes a pinhole lens and contact lens. Thecontact lens comprises an optically transparent lens body having aconcave surface adapted to the patient's eye curvature and a convexsurface. The lens has three regions: (1) an annular region of a firstoptical power; (2) at the center of said annular region, which is alsoat the optical center of said lens, a substantially pinhole-likeaperture; and (3) a second larger annular region exterior to the firstannular region.

U.S. Pat. No. 5,662,706 discloses a variable transmissivity annular masklens for the treatment of optical aberrations, such as night myopia,spherical aberration, aniridia, keratoconus, corneal scarring,penetrating keratoplasty, and post refractive surgery complication. Thelens has an annular mask having an aperture larger than conventionalpinhole contact lens. The aperture having a “soft” inside edge and whichmask has a gradually increasing transmissivity radially toward the outeredge of the mask.

U.S. Pat. No. 5,225,858 describes a multifocal ophthalmic lens adaptedfor implantation in the eye or to be disposed on or in the cornea. Thelens has an optical axis, a central zone and a plurality of annularzones circumscribing the central zone. Two of the annular zones have afirst region with a far vision correction power and a second region witha near vision correction power. In an IOL embodiment, the visioncorrection power between far and near is progressive, and each of thesecond regions has a major segment in which the near vision correctionpower is substantially constant. The power in the central zone varies.

U.S. Pat. No. 6,554,859 discloses an intraocular lens for implantationin an eye of a patient. The lens includes a multifocal optic and amovement assembly. The optic has maximum add power which is less thanthe add power required for full near vision for a pseudophakic eye. Themovement assembly is coupled to the optic and is adapted to cooperatewith the eye of the patient to effect accommodating movement of theoptic in the eye. Lens systems including two optics and two movementassemblies are also provided. The intraocular lenses and lens systemsare particularly useful when implanted in the eyes of a patient afterremoval of the natural lenses.

U.S. Pat. Nos. 6,576,012 and 6,537,317 disclose a binocular lens systemfor improving the vision of a patient. The system includes first andsecond ophthalmic lenses. Each of these lenses is adapted forimplantation in an eye or to be disposed on or in the cornea. The firstlens has a first baseline diopter power for distance vision correctionand the second ophthalmic lens has a second baseline diopter power forother than distance vision correction. The ophthalmic lenses may beintraocular lenses which are implanted in the eyes of a patient or hasnatural lenses or following removal of the natural lenses.

U.S. Pat. No. 6,474,814 discloses a multifocal ophthalmic lens withinduced aperture. The multifocal lenses are defined by nonconicalaspheric optical surfaces. Various alternative surface shapes provide acentral distance vision region surrounded by an optical step. Theoptical step has rapidly increasing power in the radial direction whichcreates an induced aperture through which the cortical elements of thevision system are induced to concentrate. The induced aperture resultsin increased clarity in distance vision. Nonconical aspheric opticalsurfaces are defined to produce the desired optical power distributions.These surface functions are also provided in form of polynomial seriesfor simplicity of use in computer driven lathes for shaping contactlenses. This technique refers to contact lenses, scleral lenses,intraocular lenses, and lenses impressed or surgically shaped within thecorneal tissue.

U.S. Pat. No. 6,527,389 describes an improved multifocal ophthalmiclens, which has a plurality of alternating power zones with acontinuously varying power within each zone, as well as in transitionfrom one zone to another. In other words, a plurality of concentriczones (at least two) are provided in which the variation from far tonear vision correction is continuous, i.e., from near correction focalpower to far correction focal power, then back to near, and again backto far, or vice versa. This change is continuous (progressive), withoutany abrupt correction changes, or “edges”. Two versions of thistechnique are disclosed. In the first version continuous, alternatingpower variation is accomplished by a continuously changing curvature ofthe lens posterior surface, thereby altering the angle of impact oflight rays on the eye. In the second version continuous, alternatingpower variation is accomplished by creating non-homogeneous surfacecharacteristics having refractive material indexes which continuouslyvary in the lens radial direction (out from the optical axis).

U.S. Pat. No. 5,715,031 discloses concentric aspheric multifocal lensdesigns which use a combination of an aspheric front surface, whichresults in aberration reduction and contrast vision enhancement, alongwith a concentric multifocal back surface, to produce a lens designwhich affords clear vision at a distance and also near without a loss incontrast which is generally typical of prior art simultaneous vision,concentric multifocal lens designs. The aspheric surface improves themodulation transfer function (MTF) of the lens eye combination whichimproves the focus and contrast of both distance and near images. Thedesign form is valid for contact lenses and intraocular lenses.

U.S. Pat. No. 6,024,447 discloses an enhanced monofocal ophthalmic lensfor providing a monofocal vision correction power with an enhanced depthof focus. The lens is adapted to be implanted into an eye, placed overthe eye, or to be disposed in a cornea of the eye. The ophthalmic lensincludes a baseline diopter power for far vision correction, a firstzone having a first vision correction power, and a second zone having asecond vision correction power. The second zone is located radiallyoutwardly of the first zone. The first zone includes a near visioncorrection power, and the second zone includes a far vision correctionpower. A maximum diopter value of the first zone is approximately 0.7diopters above the baseline diopter, and a minimum diopter value of thesecond zone is approximately 0.5 diopters below the baseline diopterpower. The first zone is adapted for focusing light at a firstpredetermined distance from the retina of the user, and the second zoneis adapted for focusing light at a second predetermined distance fromthe retina of the user. The second predetermined distance isapproximately opposite and equal to the first predetermined distance. Athird zone, which is substantially similar to the first zone, is locatedradially outwardly of the second zone, and a fourth zone, which issubstantially similar to the second zone, is located radially outwardlyof the third zone. A third vision correction power of the third zone isapproximately the same as the first vision correction power of the firstzone, and a fourth vision correction power of the fourth zone isapproximately the same as the second vision correction power of thesecond zone.

U.S. Pat. No. 6,451,056 describes an intraocular lens for increaseddepth of focus. The intraocular lens provides substantially increaseddepth of focus for accurate near and far vision with an optic muchthinner than a natural lens, the lens being rigid, vaulted posteriorlyand adapted for posterior positioning in the capsular bag. The optic ispositioned substantially farther from the cornea than a natural lens, sothat a cone of light exiting the optic to impinge upon the retina ismuch smaller than a cone of light from a natural lens. Typically, theoptic may be about 1.0 mm thick and its distance from the cornea 7.0-8.0mm.

WO 03/032825 discloses a method of designing a contact lens or othercorrection for providing presbyopia correction to a patient. The methodrelies on wavefront aberration measurement data for providing a bestform correction. Preferably the correction is in the form of amultifocal translating style alternating vision contact lens or asimultaneous vision style correcting lens. A method for designing acorrection for improving a person's vision is directed to correctinghigher order aberrations in such a manner that a residual amount of thehigher-order rotationally symmetric aberration is greater than aresidual amount of the higher-order rotationally asymmetric aberrationafter the correction. The design method is directed to correctingasymmetric higher order aberrations induced by decentering of amultifocal contact lens that has residual spherical aberration whichprovides increased depth of field.

EP 0369561 discloses a system and process for making diffractive contactand intra-ocular lenses. The optical system includes the followingprincipal elements in optical alignment along an optical axis, foraccomplishing the indicated steps of the process: a laser for emissionof ultraviolet light along the optical axis; a zone plate mask in thepath of irradiation by the laser; and an imaging lens to project, withradiation from the laser, an image of the mask on the concave innersurface of an eye lens mounted coincident with the image surface of theoptical system, thereby ablating the eye lens imagewise of the mask togenerate a phase zone plate on the eye lens. The laser beam scans thezone plate mask to generate a composite image on the image surface.Alternatively, the phase zone plate is generated on the concave surfaceof a glass blank at the image surface to form a tool from which molds,and in turn lenses, are replicated. The light source is an argonfluoride excimer laser, emitting at 193 nm. The lens is a variablemagnification lens to project various size images of the mask forproducing zone plates of various powers as desired.

The known techniques, however, suffer from such drawbacks as unavoidablescattering of a significant part of energy towards the outer regions ofa field of view of the system; the need for digital post processing;damaging the spatial frequencies transmission and the energeticefficiency.

SUMMARY OF THE INVENTION

There is accordingly a need in the art for an all-optical extended depthof focus technique.

The present invention solves the above problems by providing an imagingarrangement utilizing an optical element located adjacent to, attachedto the surface of, or incorporated within an effective aperture of theimaging arrangement. It should be noted that the term “effectiveaperture of the imaging arrangement” used herein signifies a lightcollecting aperture, which may be the actual size of an imaging lensitself or an aperture in front of the imaging lens, as the case may be,for example the eye's pupil in ophthalmic applications. It should alsobe noted that the imaging arrangement of the present invention mayutilize a an array of lenses (lenslet array), in which case an array ofoptical elements is used, each optical element being associated with acorresponding one of the lenses.

The optical element of the present invention is configured as aphase-affecting, non-diffractive, thin-layer optical element that codesthe lens aperture so as to provide an all-optical effect of extendingthe depth of focus. The optical element may be configured as aphase-only element or as a phase and amplitude affecting element. Theterm “all-optical” used herein signifies that a need for imageprocessing is eliminated or at least substantially reduced.

The optical element is thus insensitive to wavelength and polychromaticillumination, does not scatter energy towards the outer regions of thefield of view thus providing a very high energetic efficiency at theregion of interest (close to 100%), and does not require apodization. Itis important to note that such a high efficiency cannot be achieved by adiffractive optical element even if it is phase-only element, because ofthe divergence of light to unwanted diffraction orders. Since thetechnique of the present invention does not require digital postprocessing, it is adequate for ophthalmic applications or other“non-computer” based applications.

The optical element of the present invention is configured to define amask (preferably a binary mask) of spatially low frequenciestransitions. This may actually be achieved by designing the opticalelement so as to define at least one transition region (e.g., line orcircle), to be surrounded by regions of the imaging lens, in the planeof the imaging lens. This at least one region of the optical elementtogether with the imaging lens' regions define a predetermined patternformed by spaced-apart optically transparent features of differentoptical properties (i.e., differently affecting the phase of lightpassing through the imaging lens arrangement).

The position(s) of the transition region(s) of the optical elementwithin the imaging lens plane (i.e., the affective aperture plane) areselected, considering at least the affective aperture size of theimaging lens. These positions are appropriately selected so as togenerate proper phase interference relation between light portionspassing through different regions of the lens arrangement correspondingto the different features of the pattern, to thereby enable reducing aquadratic phase factor resulting from light getting out of focus of theimaging lens and thus maximize a defocused optical transfer function(OTF) of the imaging lens arrangement.

As indicated above, in order to design the optimal configuration for theextended depth of focus (EDOF) optical element, the effective apertureof the imaging lens is to be taken into consideration. The optical powerdistribution of the imaging lens and/or focal length may also be takeninto consideration: since the EDOF has no optical power, it may be addedto an imaging lens in order to shift the range of extended depth offocus around a certain given optical power.

The optimal geometry and dimensions of the EDOF element (i.e., at leastone transition region) are determined using an optimization algorithm(based on a numerical or analytical approach, resulting in a spatiallylow frequency all-optical extended depth of focus), which determines Nposition(s) for the transition region(s) of the element within a givenimaging lens (i.e., for a given effective aperture size).

Considering ophthalmic applications, where the effective aperture of thelens (eye pupil, or contact lens, or lens of spectacles) can be definedby a certain relatively narrow range of values common for most ofpatients, the EDOF of the present invention can be designed to beuniversal for a great amount of patients. Such a universal EDOF isconfigured to allow the depth of focus region equivalent to 5 dioptersfor the effective aperture of 2-3 mm. For a smaller percentage ofpatients having a higher difference between the near and far vision, thedesign of the EDOF element takes into account the optical power of theimaging lens with which the element is associated.

The position of the transition(s) (being pi-phase transition for acertain wavelength for which the EDOF is designed) generates invarianceto quadratic phase distortions (which multiply the CTF of the imaginglens, corresponding to the effect of getting out of focus) under theoperation of auto correlation. Due to the fact that the aperture mask(formed by the EDOF and imaging lens) is constructed out of spatiallylow-frequency transitions, it does not spread energies away from thezero order of diffraction and its energetic efficiency is close to 100%.

It should be noted that auto correlating the CTF is done to compute theoptical transfer function (OTF) of the imaging system. The position ofthe EDOF transition(s) may be computed using iterative algorithm inwhich M positions are examined and eventually those of them areselected, which provide maximal contrast of the OTF under a set of outof focus locations. The meaning of OTF's contrast optimization(maximizing) is actually having the out of focused OTF bounded as muchas possible away from zero.

The extended depth of focus (EDOF) element of the present invention isconfigured to generate proper phase interference relation allowingsignificant cancellation of the quadratic phase factor obtained due togetting out of focus. The EDOF element is a phase-affecting element(e.g., phase-only binary mask element), which is neither a refractivenor a diffractive element. In contrast to a refractive element, the EDOFfilter of the present invention can be produced as a thin phase layerconstructed in a low-cost lithographic technique or stamping with thethickness of the phase layer being of only one wavelength (e.g., around0.5 micron in the case of ambient light illumination), similar to thefabrication approaches used for the conventional diffractive opticalelements. On the other hand, in contrast to diffractive opticalelements, the EDOF of the present invention has the spatial feature(s)of very low frequency. The element contains only very limited number offeatures and periods at low spatial frequency (period of about 1,000wavelengths). The property of the optical element of the presentinvention allows for obtaining truly energetic efficient EDOF, since notonly all the energy is passed through the element itself (it issubstantially phase only) but also all of the energy is concentrated atthe proper transversal and longitudinal region of interest (in contrastto a diffractive element that has energetic split either betweenmultiple longitudinal focal planes or between traversal diffractionorders).

Hence, high energetic efficiency (close to 100%) of the optical elementof the present invention provides extended depth of focus, in contrastto approaches based on the use of diffractive optical elements thatsplit the energy between several diffraction orders/focal planes andthat are basically equivalent to smaller lens aperture (also havinglarger depth of focus). In addition, the low spatial frequency of theinvented approach eliminates its sensitivity to wavelength andpolychromatic illumination which is a problematic topic with diffractiveoptical elements. Additionally, it is important to note that theinvented approach is an all-optical technique that does not requirenumerical computation, and when it is used for ophthalmic applicationsit does not assume brain based decoding or adaptation process since anextended depth of focus image is identical to the image of an objectitself.

There is thus provided according to one broad aspect of the presentinvention, an imaging arrangement comprising: an imaging lens assemblyincluding at least one lens having a certain affective aperture, and atleast one optical element associated with said at least one lens andconfigured to provide an extended depth of focus of the imagingarrangement, said optical element being configured as a phase-affecting,non-diffractive optical element defining a spatially low frequency phasetransition, said optical element together with its associated lensdefining a predetermined pattern formed by spaced-apart opticallytransparent features of different optical properties, position of atleast one phase transition region of the optical element within the lensplane being determined by at least a dimension of said affectiveaperture.

According to another broad aspect of the invention, there is provided animaging arrangement comprising: an imaging lens assembly including atleast one lens having a certain affective aperture, and at least oneoptical element associated with said at least one lens and configured toprovide an extended depth of focus of the imaging arrangement, saidoptical element being configured as a phase-only, non-diffractive binarymask defining a spatially low frequency phase transition, said opticalelement together with its associated lens defining a predeterminedpattern formed by spaced-apart optically transparent features ofdifferent optical properties, position of at least one phase transitionregion of the optical element within the lens plane being determined byat least a dimension of said affective aperture.

According to yet another aspect of the invention, there is provided animaging arrangement comprising: an imaging lens assembly including atleast one lens having a certain affective aperture, and at least oneoptical element associated with said at least one lens and configured toprovide an extended depth of focus of the imaging arrangement, saidoptical element being configured as a phase-affecting, non-diffractiveoptical element defining a spatially low frequency phase transition,said optical element together with its associated lens defining apredetermined pattern formed by spaced-apart optically transparentfeatures of different optical properties, position of at least one phasetransition region of the optical element within the lens plane beingdetermined by at least a dimension of said affective aperture such thatthe optical element produces proper phase interference relation betweenlight portions passing through different regions of the imagingarrangement corresponding to the different features of the pattern tothereby reduce a quadratic phase factor resulting from light getting outof focus of the imaging lens and maximize a defocused optical transferfunction (OTF) of the imaging lens arrangement by providing the out offocus OTF as much as possible away from zero.

According to yet another broad aspect of the invention, there isprovided an imaging arrangement comprising an imaging lens assemblyincluding at least one lens having a certain affective aperture, and atleast one optical element associated with said at least one imaging lensand configured to provide an extended depth of focus of the imagingarrangement, said optical element being configured as a phase-affecting,non-diffractive element defining a certain pattern of spatially lowfrequency phase transitions within a plane of the imaging lens, suchthat said optical element together with its associated imaging lensdetermine a predetermined pattern formed by spaced-apart opticallytransparent features differently affecting phase of light passingthrough the imaging arrangement, positions of the phase transitions ofthe optical element within the imaging lens plane being determined by atleast a dimension of said affective aperture to reduce sensitivity ofthe imaging arrangement to shifts of a Coherent Transfer Function (CTF)of the imaging lens while getting out of focus.

According to yet another broad aspect of the invention, there isprovided an imaging arrangement comprising an array of lenses eachhaving a certain affective aperture, and an array of optical elementseach optical element being associated with one lens of the lenslet arrayand being configured to provide an extended depth of focus of theimaging arrangement, said optical element being configured as aphase-affecting, non-diffractive optical element defining a spatiallylow frequency phase transition, said optical element together with itsassociated lens defining a predetermined pattern formed by spaced-apartoptically transparent features of different optical properties, positionof at least one phase transition region of the optical element withinthe lens plane being determined by at least a dimension of saidaffective aperture.

According to yet another aspect of the invention, there is provided animaging lens for use in patients' spectacles, the imaging lens beingconfigured to define a certain affective aperture and carrying anoptical element configured to provide an extended depth of focus, saidoptical element being configured as a phase-affecting, non-diffractiveoptical element defining a spatially low frequency phase transition,said optical element together with its associated lens defining apredetermined pattern formed by spaced-apart optically transparentfeatures of different optical properties, position of at least one phasetransition region of the optical element within the lens plane beingdetermined by at least a dimension of said affective aperture.

According to yet another aspect of the invention, there is provided adisplay device carrying an imaging arrangement, which comprises an arrayof imaging lenses each having a certain affective aperture, and an arrayof optical elements each associated with a corresponding one of saidlenses and configured to provide an extended depth of focus, saidoptical element being configured as a phase-affecting, non-diffractiveoptical element defining a spatially low frequency phase transition,said optical element together with its associated lens defining apredetermined pattern formed by spaced-apart optically transparentfeatures of different optical properties, position of at least one phasetransition region of the optical element within the lens plane beingdetermined by at least a dimension of said affective aperture.

It should be understood that such a display device may be a dynamic-typedevice for use with or being part of an electronic device (such as amobile phone) or may be a static display device.

According to yet another aspect of the invention, there is provided asystem for creating an image of an object on a detector plane, thesystem comprising an imaging lens arrangement formed by an imaging lensassembly including at least one lens having a certain affective apertureand at least one optical element configured to provide an extended depthof focus of the imaging arrangement, said optical element beingconfigured as a phase-affecting, non-diffractive element defining aspatially low frequency phase transition, said optical element togetherwith its associated imaging lens defining a predetermined pattern formedby spaced-apart optically transparent features of different opticalproperties, position of at least one phase transition region of theoptical element within the imaging lens plane being determined by atleast a dimension of said affective aperture such that the opticalelement produces proper phase interference relation between lightportions passing through different regions of the imaging arrangementcorresponding to the different features of the pattern to thereby enablereducing a quadratic phase factor resulting from light getting out offocus of the imaging lens and maximize a defocused optical transferfunction (OTF) of the imaging arrangement.

According to yet another aspect of the invention, there is provided anoptical element for use with an imaging lens for extending depth offocus of imaging, the optical element being configured as aphase-affecting, non-diffractive optical element defining apredetermined pattern of spatially low frequency phase transitions, saidpattern being defined by an affective aperture of the given imaginglens.

According to yet another aspect of the invention, there is provided anoptical element for use with an imaging lens for extending depth offocus of imaging, the optical element being configured as a phase-only,non-diffractive binary element defining a predetermined pattern ofspatially low frequency phase transitions, said pattern being defined byan affective aperture of the given imaging lens. According to yetanother aspect of the invention, there is provided an optical elementfor extending depth of focus of imaging, the optical element beingconfigured as a phase-affecting, non-diffractive optical elementdefining a spatially low frequency phase transition.

According to yet another aspect of the invention, there is provided anoptical element for extending depth of focus of imaging, the opticalelement being configured as a phase-affecting, non-diffractive opticalelement defining a spatially low frequency phase transition, the opticalelement defining a predetermined pattern of phase transition regions,said transition regions being arranged in accordance with an affectiveaperture of a given imaging lens for which the optical element isdesigned, so as to provide said transition regions of the opticalelement within predetermined positions in the imaging lens plane, toprovide periodic replication of a lateral phase shape of a light fieldpropagating through the imaging lens with said optical element.

According to yet another aspect of the invention, there is provided anoptical element for extending depth of focus of imaging, the opticalelement being configured as a phase-only, non-diffractive binary elementdefining a spatially low frequency phase transition, the optical elementdefining a predetermined pattern of phase transition regions, saidtransition regions being arranged in accordance with an affectiveaperture of a given imaging lens for which the optical element isdesigned, so as to provide said transition regions of the opticalelement within predetermined positions in the imaging lens plane, toprovide periodic replication of a lateral phase shape of a light fieldpropagating through the imaging lens with said optical element.

According to yet another aspect of the invention, there is provided amethod for providing a certain extended depth of focus of an imagingsystem, the method comprising applying an aperture coding to an imaginglens having a certain effective aperture, by applying to the imaginglens a phase-affecting non-diffractive optical element configured todefine a spatially low frequency phase transition arrangement andthereby provide a predetermined pattern of spaced-apart substantiallyoptically transparent features of different optical properties withinthe imaging lens plane, thereby producing phase interference relationbetween light portions passing through different regions of the lensarrangement corresponding to the different features of the pattern so asto reduce a quadratic phase factor resulting from light getting out offocus of the imaging lens and maximize a defocused optical transferfunction (OTF) of the imaging lens arrangement.

According to yet another aspect of the invention, there is provided amethod for providing a certain extended depth of focus of an imagingsystem, the method comprising designing a phase-affectingnon-diffractive optical element to be used with an imaging lens having acertain effective aperture, said designing comprising selecting Npositions for phase transitions within the imaging lens effectiveaperture as those providing maximal contrast of an Optical TransferFunction (OTF) of the imaging system under a set of out of focuslocations, thereby providing the out of focus OTF as much as possibleaway from zero.

BRIEF DESCRIPTION OF THE DRAWINGS

In order to understand the invention and to see how it may be carriedout in practice, preferred embodiments will now be described, by way ofnon-limiting example only, with reference to the accompanying drawings,in which:

FIG. 1A is a schematic illustration of an example of an imaging systemutilizing an imaging lens arrangement configured according to thepresent invention;

FIG. 1B schematically illustrates another example of an imaging lensarrangement of the present invention;

FIG. 1C schematically illustrates yet another example of an imaging lensarrangement of the present invention, suitable to be used with a displaydevice;

FIGS. 1D and 1E show two examples, respectively, of the optical elementof the present invention being implemented integral with an imaginglens;

FIGS. 2A to 2C show three examples, respectively, of the contour of theoptical element of the present invention suitable to be used in theimaging lens arrangement;

FIGS. 3A to 3D illustrate the effect of the present invention ascompared to the conventional approach;

FIGS. 4A to 4I exemplify face images obtained with the out of focusparameter 4ψ/D² varying from −0.2 (FIG. 4A) up to 0.2 (FIG. 4I) at stepsof 0.05, for the case where the optical element of the present inventionis used;

FIGS. 5A to 5I exemplify face images obtained with the out of focusparameter 4ψ/D² varying from −0.2 (FIG. 5A) up to 0.2 (FIG. 5I) at stepsof 0.05, for the case where no optical element of the present inventionis used;

FIG. 6 shows the results of examining the sensitivity of the opticalelement to wavelength variations;

FIGS. 7A to 7D show experimental results for imaging a Rosette with andwithout the EDOF element of the invention: FIG. 7A corresponding to thein focus position of Rosette with no EDOF element, FIG. 7B correspondsto in-focus position with the EDOF element, FIG. 7C corresponds to theout of focus position of Rosette with no EDOF element, and FIG. 7Dcorresponds to the out of focus position with the EDOF element;

FIGS. 8A to 8D and FIGS. 9A to 9H show experimental verification of theextended depth of focus technique of the present invention forpolychromatic spatially non coherent illumination;

FIG. 10A illustrates the performance of the ophthalmic depth of focusapplication of the present invention, for the case where the opticalelement is attached to a contact lens;

FIG. 10B illustrates the performance of the ophthalmic depth of focusapplication of the present invention, for the minimal range at whichfocus is obtained with and without the optical element of the presentinvention;

FIGS. 11A and 11B present two images of a typical visual acuityresolution target, respectively, obtained by the technique of theinvention and by an optical system with presbyopia with 1.75 Diopters;

FIGS. 12A-12B and 13 show the ophthalmic experimental results (visualacuity diagrams) obtained using phase elements of the present inventionfor a group of persons;

FIGS. 14A and 14B present the ophthalmic experimental results for thetechnique of the present invention showing improvement of irregularastigmatism; and

FIGS. 15A and 15B present the ophthalmic experimental results for thetechnique of the present invention showing improvement of regularastigmatism.

DETAILED DESCRIPTION OF THE INVENTION

Referring to FIG. 1A, there is schematically illustrated an imagingsystem 10 utilizing an imaging lens arrangement 12 of the presentinvention. The imaging system 10 is formed by an object 13 that is to beimaged, the imaging lens arrangement 12, and a light detector unit 16.The imaging lens arrangement 12 includes a certain number of lenses 12A(generally at least one lens, single lens being shown in the presentexample) having a certain effective aperture D (which in the presentexample is the lens diameter), and a certain number of optical elements12B (single element in the present example) associated with the lens(es)12A. Such optical element 12B is configured and operable as an extendeddepth of focus (EDOF) element.

The optical element 12B is configured in accordance with the parametersof the lens 12A, i.e., its effective aperture and optionally also theoptical power distribution and/or focal length. The optical element 12Bis configured as a phase-affecting non-diffractive mask. Preferably, asshown in the present example, the mask 12B is implemented integral withthe lens, namely as a pattern on the lens surface.

Generally, the mask 12B may be a separate element attached to the lensor located close thereto. This is illustrated in FIG. 1B showing animaging system 100 utilizing a lens arrangement 112 that includes a lens12A and a phase-affecting non-diffractive optical element 12B locatedclose to the lens in front thereof.

FIG. 1C shows schematically an imaging system 200 according to yetanother example of the invention. Here, an imaging lens arrangement 212includes an array of lenses 12A, formed by four such lenses L₁, L₂, L₃and L₄ in the present example, and an array 12B of optical elements OE₁,OE₂, OE₃ and OE₄ each associated with a corresponding lens of thelenslet array.

Such system 200 may for example be used with a display panel or screen13 (constituting an object) aimed at facilitating the imaging of thedisplay/screen (e.g., of a mobile phone device) by people having closevision problems. The imaging arrangement 212 is accommodated at a smalldistance (a few millimeters from a surface 13′ of the display panel 13.Also, in the present example the optical elements' array 12B is locateddownstream of the lenslet array 12A with respect to light propagationfrom the object 13 towards a light detector 16 (patient's eye). The useof such lenslet' and EDOF elements' arrays provides for bringing theclosest focus plane FP of the imaging arrangement 212 as close aspossible to the object 13 plane, so that people with the close visionproblems as well as people with normal vision will be able to see thescreen. In addition, bringing the closest focus plane closer to theobject plane reduces the demagnification ratio of the object that is tobe focused.

Preferably, the optical element 12B is configured as a phase-only binarymask. It should, however be noted that generally the element 12B may beconfigured as a phase and amplitude mask.

The optical element 12B is configured to define at least one spatiallylow frequency transition region, and, together with the lens 12Aregions, define a predetermined pattern of spaced-apart substantiallyoptically transparent features differently affecting the phase of lightpassing therethrough. The pattern is thus formed by one or moretransition regions of the optical element, spaced by the regions of thelens, in the imaging lens plane. The transition regions are pi-phasetransitions for a certain wavelength for which the mask 12B is designed.The arrangement of these transition regions (positions within the lens12A plane) is determined by the effective aperture of the given imaginglens 12A (and possibly also optical power of the lens) so as to maximizethe defocused OTF of the entire imaging arrangement. To this end, thepattern is such as to generate proper phase interference relationbetween light portions passing through different regions of the lensarrangement to thereby enable reducing a quadratic phase factorresulting from light getting out of focus of the imaging lens.

As shown in FIGS. 1D and 1E, the optical element may be implemented as asurface relief on the imaging lens (FIG. 1D), namely, a pattern ofspaced-apart regions R₁ and R₂ of variable lens thickness; or as apattern of lens regions R′₁ and R′₂ made of materials with differentrefractive indices n₁ and n₂ (FIG. 1E). In the case of differentrefractive index materials, a certain optically transparent material ofa refractive index different from that of the lens may be coated onselective spaced-apart regions of the lens surface.

FIGS. 2A to 2C show two specific but not limiting examples,respectively, of the contour of the optical element 12B. In the exampleof FIG. 2A, the mask 12B is designed as an annular transition region 14(generally, at least one such region; an array of concentric rings maybe used as well). In the example of FIG. 2B the mask is designed as agrid formed by two mutually perpendicular pairs of bars (lines) B₁-B′₁and B₂-B′₂. In the example of FIG. 2C, the element 12B is a mask formedby a two-dimensional array of basic grid-elements BE. For example, thetransition regions along the bar line are pi-phase transitions and theregions of intersection between the perpendicular bars are zero-phasetransitions. The optimized contour for the optical element is obtainedsolving an algorithm, which will be described further below.

It should be noted that the mask (pattern) may and may not besymmetrical relative to the center of the lens. In such an arrangement,for example, the four π-phase bars, two vertical (along Y-axis) and twohorizontal (along X-axis) bars, that are illustrated in FIG. 2A, may beshifted transversally along the x-y plane to be not centered around thecenter of the lens.

It should also be noted, although not specifically shown, that thepattern may be configured to define microstructures inside the phasetransition region (e.g., inside the pi-phase transition ring of FIG.2A), namely, each phase transition region may be of a variable spatiallylow frequency of phase transition such as for example π/2, π, . . . .

The present invention provides the EDOF element 12B in the form of amask of N segments within the effective aperture of the imaging lens12A. It should be understood that instead of having a mask that blocksenergy in some of segments and transmits in the other, the inventionprovides the substantially phase-only, non-diffractive mask 12B, that iseither 1 or (−1) depending on the segment.

As indicated above, the mask 12B is designed to maximize the defocusedOTF of the imaging system, by generating invariance to quadratic phasefactor (which factor is generated when the image is defocused andmultiplies the CTF of the imaging lens). To this end, in order tooptimally design the mask 12B, a search is made for the segments thatwill obtain the transmission value of (−1) such that the OTF, due to theout of focus distortion, is bounded as much as possible away from zero.Since the mask 12B is a binary phase mask, no energy efficiencyconsideration is used (the transmission is 100%). Following thesecriteria, a search is made over all the possibilities and combinationsfor the aperture coding mask. The out of focus distortion is modeled bymultiplying the aperture with the following expression:

$\begin{matrix}{{\overset{\sim}{D}(v)} = {\exp\left( \frac{i\; 4\Psi\; v^{2}}{D^{2}} \right)}} & (1)\end{matrix}$wherein {tilde over (D)}(v) is the CTF of the imaging lens 12Acorresponding to the out of focus position of the object being imaged, Dis the diameter of the imaging lens 12A (generally, the effectiveaperture of the lens), v is the coordinate of the aperture of the lens(in the plane of CTF), and ψ is the phase factor representing the amountof getting out of focus:

$\begin{matrix}{\Psi = {\frac{\pi\; D^{2}}{4\;\lambda}\left( {\frac{1}{u} + \frac{1}{v} - \frac{1}{F}} \right)}} & (2)\end{matrix}$wherein λ is the wavelength, u is the distance between the imaging lens12A and the object 13, v is the distance between the imaging lens 12Aand the sensor 16 (detector), and F is the focal length of the imaginglens. It should be noted that the term “imaging lens” refers here to theeffective aperture thereof.

When imaging condition is fulfilled:

$\begin{matrix}{{\frac{1}{u} + \frac{1}{v}} = \frac{1}{F}} & (3)\end{matrix}$the distortion phase factor ψ equals zero.

The OTF is computed by auto-correlating the CTF with itself:OTF(v)=CTF(v)

CTF(v)  (4)

The auto correlation operation consists of shifting two CTF functions tothe opposite directions, respectively, and then multiplying and summingthe result. The so-obtained OTF relates to a spatial frequency thatcorresponds to the amount of the shift. At high frequencies (largeshifts), the multiplication and the summing are averaged to zero in thecase of out of focus. Hence, the OTF does not transmit high frequencieswhen the image is defocused.

The phase mask (e.g., ring) of the present invention is aimed atreducing the high-frequency cancellation at large shifts of the CTF (theOTF is an auto correlation of the CTF). To this end, the mask isconfigured to invert the sign of part of the light field that before(i.e., pure lens with no EDOF correction) was averaged to zero (and thisis why the OTF did not transmit the high spatial frequencies).

The OTF is the Fourier transform of the intensity point spread function,and it is used to express the spatial-frequencies transmission functionfor intensity, when incoherent illumination is applied. Thus, themathematical formulation for maximizing the OTF is as follows:

$\begin{matrix}{\max\limits_{a_{n}}\left\{ {\min\left\{ {\left\lbrack {{\overset{\sim}{D}(v)}{\sum\limits_{n = 1}^{N}{a_{n}{{rect}\left( \frac{v - {n\;\Delta\; v}}{\Delta\; v} \right)}}}} \right\rbrack \otimes \left\lbrack {{\overset{\sim}{D}(v)}{\sum\limits_{n = 1}^{N}{a_{n}{{rect}\left( \frac{v - {n\;\Delta\; v}}{\Delta\; v} \right)}}}} \right\rbrack} \right\}} \right\}} & (5)\end{matrix}$i.e., find the values for a_(n) that provide maximum for the minima ofthe auto correlation expression where a_(n)=(1,−1) (it equals either 1or −1).

It should be noted that the above-described iterative numericalalgorithm is a specific but not limiting example of defining the EDOFelement configuration. Other techniques can be used as well, for examplenumerical approached based on entropy minimization, or maximallikelihood, or other numerical or analytical approaches, resulting in aspatially low frequency all-optical extended depth of focus.

FIGS. 3A to 3D illustrate the effect of the present invention. Threeexamples of absolute value of the OTF (called Modulation TransferFunction—MTF) are obtained for different phase factor values: ψ=1.6 inFIG. 3A; ψ=4.8 in FIG. 3B; ψ=9.8 in FIG. 3C and ψ=12.8 in FIG. 3D. Ineach of these figures, curve C₁ corresponds to the MTF while at thein-focus state, curve C₂ corresponds to the defocused MTF of an imagingsystem without the use of the correction optical element (EDOF element)of the present invention (mask 12B in FIG. 1), and curve C₃ correspondsto the defocused MTF of the system with the correction element.

The transversal invariance may be obtained using the phase elementproducing periodic replication of the phase shape, namely lateralreplication of the phase shape. Turning back to FIG. 2C exemplifying amask formed by a two-dimensional array of basic elements BE, when largelateral shifts (high frequencies) exclude part of the phase shape, acomplimentary part is inserted from another spatial period of the maskthus producing the phase period by replication. The replication of thebasic period of the transitions (that of the basic element BE) thusreduces the sensitivity to lateral shifts. The longitudinal invarianceis obtained as follows: Given the longitudinal distance between thephase element and a sensor (the imaging lens plane or the effectiveaperture plane), which is the lens of the human eye in case ofophthalmic applications, free space propagation of the mask function forthis distance is considered. The result is a phase and amplitudedistribution. The amplitude is dropped, leaving only the phase profile.In many cases, binarization of the phase function may providesufficiently good results as well. The binarization realizes spatialmask which is easier for fabrication.

Reference is made to FIGS. 4A-4I and FIGS. 5A-5I illustrating how a faceimage looks like when the defocusing parameter 4ψ/D² is varied from −0.2(FIGS. 4A and 5A) up to 0.2 (FIGS. 4I and 5I) at steps of 0.05. FIGS.4A-4I show the case where the mask (optimally designed) of the presentinvention is used, and FIGS. 5A-5I shows the case where no such aperturecoding mask is used. In the present example, the EDOF element configuredsimilar to that of FIG. 2B was used. As clearly seen in the figures, adifference in distortions between images of FIGS. 4A-4I and 5A-5I existsdue to the aperture coding mask of the present invention.

FIG. 6 shows the results of examining the sensitivity of the coding mask(EDOF element) of the present invention to wavelength variations. In thepresent example, an imaging lens arrangement (imaging lens with a codingmask) was illuminated with wavelength λ₁=0.8λ₀, wherein λ₀ is thewavelength for which the mask was designed and fabricated to presentpi-phase transition(s), and the defocusing parameter of 4ψ/D²=0.15 wasused. As could be seen, the out of focus distortion obtained due to theusage of the mask is still very low despite the fact that the mask is nolonger optimized (since the mask pattern features are pi-phasetransitions for λ₀ and not for λ₁).

FIGS. 7A-7D show another experimental results obtained for imaging aRosette. Here, FIG. 7A shows an image corresponding to the in focusposition of the Rosette obtained with no EDOF element of the invention;FIG. 7B shows an in-focus image obtained with the EDOF element; FIG. 7Ccorresponds to the out of focus position of the Rosette with no EDOFelement; and FIG. 7D shows an image of the out of focus Rosette obtainedwith the EDOF improvement of the present invention. In the presentexample, the EDOF element configured similar to that of FIG. 2A wasused. As shown, the use of the EDOF element of the present inventionprovides improvement in spatial high frequencies and the effect on theinput when the system is in focus.

It should be noted that in all the images presented in FIGS. 4A-4I,5A-5I, 6 and 7A-7D, showing sufficient extension of the depth of focus,no digital post processing was applied. Applying such processing mightfurther improve the obtained results.

The inventor has performed experimental verification of the extendeddepth of focus approach for polychromatic spatially non coherentillumination (general lighting). The experimental conditions were asfollows: the focal length of the imaging lens F=90 mm, the distancebetween the imaging lens and the object v=215.9 mm, the distance betweenthe imaging lens and detector (CCD) u=154.3 mm, the aperture of theimaging lens D=16 mm. Thus, the measurement for the phase distortion ψequals to 13 for the case where the object is moved a distance of 1.5 mmfrom the in cofus plane, and ψ=17 for moving the object a distance of 2mm. The value of the phase factor ψ is computed following equation 2above and using the distances and the diameter of the lens (affectiveaperture of the lens) in the optical system. The experimental resultsunder these conditions are shown in FIGS. 8A-8D and FIGS. 9A-9H. In thepresent example, the EDOF element configured similar to that of FIG. 2Awas used.

Here, FIG. 8A corresponds to an in-focus position without the use of theoptical element of the present invention; FIG. 8B corresponds to thein-focus with such element, FIG. 8C corresponds to the defocusedposition without the optical element at ψ=13 (+1.5 mm), and FIG. 8Dcorresponds to the defocused position with the optical element at ψ=13(+1.5 mm).

FIG. 9A shows an in focus image obtained without the optical element;FIG. 9B shows the defocused image at ψ=13 (+1.5 mm) without the element;FIG. 9C shows the defocused image at ψ=17 (+2 mm) without the element;FIGS. 9D-9F correspond to FIGS. 9A-9C but with the optical element; FIG.9G shows the defocused image at ψ=13 (+1.5 mm) obtained without theelement with polychromatic illumination; FIG. 9H shows the defocusedimage at ψ=13 (+1.5 mm) obtained with the optical element forpolychromatic illumination.

As indicated above, the imaging lens arrangement of the presentinvention may be used for ophthalmic applications. In order to allowinsertion of the imaging lens arrangement into the eye, the surface ofthe lens arrangement is to be flat. The fabrication techniques suitableto manufacture such an imaging lens arrangement (i.e., flat patternedimaging lens) include for example etching (wet or dry) or laser drillingor lathe grinding to obtain the desired spatial structure (surfacerelief), and then filling the evacuated volume by a material of arefraction index different from that of the lens, providing a refractionindex difference is such that the outer region of the mask is flat whilethe desired phase difference is generated, required as buffering phaseregion that generates proper equalization between regions of the lensaperture for the interference effect. Another realization could be bydiffusion or photo polymerization that does not include developing orremoving of the polymerized material. Yet another approach which isrelated to eye surgery could be by implanting artificial tissue havingdifference in refraction index in comparison to the existing tissue ofthe eye. The EDOF element of the present invention (having no opticalpower) is added to the focal power of a certain lens which is to beobtained. For example, if a patient needs −1 diopter glasses and 3diopters glasses for near and far visions, the EDOF element of thepresent invention may be appropriately designed to be used on either oneof these glasses, being configured in accordance with the respectivelens aperture to allow a depth of focus region equivalent to 5 diopters.Actually, in this specific example, a 1 diopter glasses with the EDOFelement of the present invention can be used, where the EDOF element isoperating around the optical power of the lens (1 diopter) and providesthe depth of field region from −1.5 to 3.5 diopters. Hence, the patientmay use only one pair of glasses with 1 diopter. This focal power of theglasses (imaging lens) will be added to the EDOF element. Such an EDOFelement maximizes the defocused OTF of the lens arrangement(appropriately modulates the CTF profile of the imaging lens of therespective glasses) by generating proper phase interference relationbetween light portions passing through different regions of the lens, toreduce a quadratic phase factor resulting from light getting out offocus of the imaging lens. The inventor has found that for most patientsa common EDOF element configuration can be used, preferably as that ofFIG. 2C. Turning back to FIG. 2C, the basic period (of the basic elementBE) is about 3 mm, a distance between two adjacent bars is about 1.875mm, and the bar thickness is about 0.375 mm.

If the EDOF element with its range of depth of focus is used on top of alens in ophthalmic applications, such as a contact lens, then it may betranslated into Diopters range. The diameter of the eye lens (effectiveaperture of the imaging lens) varies from 2 mm up to 6-7 mm depending onthe lighting conditions. The optical element generates a Diopter rangewithin which the image is in focus. The inventor has found that for theresulted range of the phase factor ψ (about up to 17) for lightenedenvironment in which the eye pupil has a diameter of 2 mm, the obtainedDiopter range P is more than 5 (from −2.5 up to 2.5). The simulationsfollowed the formula:

$\begin{matrix}{P = \frac{4{\Psi\lambda}}{\pi\; D^{2}}} & (6)\end{matrix}$

FIGS. 10A-10B present the simulation results visualizing the performanceof the ophthalmic depth of focus application of the present invention.The simulation of FIG. 10A corresponds to the overall Diopter rangeobtained due to the fact that the EDOF element is attached to a contactlens. The diameter of the eye lens varies from 2 mm up to 6-7 mmdepending on the lighting conditions. The simulations follow Eq. 6above.

In the simulation of FIG. 10B, an imaging lens with a fixed focal lengthis used. If the distance between the lens and sensor equals to its focallength (v=F) then the image will be in focus starting from a certaindistance, u_(min), up to infinity, wherein the distance u_(min) isdetermined as:

$\begin{matrix}{u_{\min} = {\frac{1}{\frac{4{\lambda\Psi}}{\pi\; D^{2}} + \frac{1}{F} - \frac{1}{v}} = \frac{\pi\; D^{2}}{4{\lambda\Psi}}}} & (7)\end{matrix}$and for v=F one obtains:

$\begin{matrix}{u_{\min} = \frac{\pi\; D^{2}}{4{\lambda\Psi}}} & (8)\end{matrix}$

The chart for u_(min) with and without the EDOF element of the presentinvention is plotted in FIG. 10B. As could be seen, the minimal distanceis much smaller when the invented element is in use. Thus, the overallrange of focus is much larger. It should be noted that for the humaneye, v=15 mm.

Turning back to FIG. 1C exemplifying an imaging arrangement of thepresent invention formed by a lenslet array and an EDOF elements' array(suitable to be used with a display panel or screen), the requiredparameters of the imaging arrangement can be estimated as follows:

Let us assume that u, which is the distance between the screen 13 andthe lenslet array 12A is about 2 mm; v, which is the distance betweenthe screen 13 and the closest focus plane FP is 40 cm; and R, which isthe distance between the eye 16 and the closest focus plane FP, is about1 m. The object 13 is constituted by the display of the mobile phone orthe screen. Basically, the lenslet array 12A images the object plane 13on the closest focus plane FP, i.e.:

${\frac{1}{u} - \frac{1}{v}} = \frac{1}{f}$ $f = \frac{u\; v}{v - u}$which provides f=2.01 mm.

The defocusing parameter is defined as:

$\Psi = {\frac{\pi\; D^{2}}{4\lambda}{{\frac{1}{u} - \frac{1}{v} - \frac{1}{f}}}}$where λ is the wavelength.

With the use of EDOF, this parameter can reach the value of 15 andwithout the EDOF element—the value of 2-3 without distorting the imagequality. The diameter, D, of the lenses in the lenslet array can befound such that the minimal value for the distance between the screen 13and the closest focus plane FP, (v_(min)), will be very close to theobject plane 13 to have minimal demagnification. The demagnificationfactor is:

$M_{T} = \frac{v_{\min}}{u}$

To have v_(min)=u=2 mm, one needs:

$D = \sqrt{\frac{{\Psi\lambda}\; f}{\pi}}$

This yields:

$D = {\sqrt{\frac{{15 \cdot 0.5}\mspace{14mu} µ\;{m\; \cdot 2.01}\mspace{14mu}{mm}}{\pi}} = {70\mspace{14mu} µ\; m}}$

It should be noted that without the EDOF element the minimal distance vwould have been:

$\begin{matrix}{v_{\min} = \frac{1}{\frac{1}{u} - \frac{1}{f} - \frac{\Psi_{\max}\lambda}{\pi\; D^{2}}}} \\{= \frac{1}{\frac{1}{2\mspace{14mu}{mm}} - \frac{1}{2.01\mspace{14mu}{mm}} - \frac{{2 \cdot 0.5}\mspace{14mu} µ\; m}{\pi \cdot \left( {70\mspace{14mu} µ\; m} \right)^{2}}}} \\{= {16\mspace{14mu}{mm}}}\end{matrix}$which means a demagnification factor of 8 (16 mm/2 mm). Such ademagnification would not have allowed seeing the characters in thedisplay.

Attachment of the lenslet array 12A to the screen decreased the visibleresolution. The resolution of such an imaging system is limited by thefactor of:

${\delta\; x} = {{{1.22 \cdot \lambda}\frac{f}{D}} = {{{1.22 \cdot 0.5}\mspace{14mu} µ\; m\frac{2.01\mspace{14mu}{mm}}{70\mspace{14mu} µ\; m}} = {17.5\mspace{14mu}{mm}}}}$

Since the details appearing in the screen are larger than that, theresolution is not damaged by the imaging lenslet array.

Following the computations presented above, a person with normal visionthat will focus his eyes on the screen (or on a plane positioned 2 mmbehind it) will see the image in focus as well.

The technique of the present invention could be barrier breaking in avast set of applications including, but not limited to, the following:conventional office devices containing camera such as camcorders,scanners (e.g., barcode scanners) and web cams; conventional imagingsystems including camera and detectors, i.e. cellular cameras, carcameras, surveillances cameras, machine vision, photography, HDTV, videoconferences, radar imaging systems (that typically suffer from defocusproblems), endoscopy and passive bio medical inspections, tomography,display panels, etc. The usage of the depth of focus extending elementof the present invention in endoscopy and passive biomedical inspectionsallows for in-body imaging to see organs in focus that otherwise arenot, since there is no control on the exact position of the medicalapparatus. Some other possible applications of the present inventioninclude correcting chromatic aberrations in various optical systems, forexample in optical communication; media reader/writers used withinformation carriers such as conventional DVD, or multi-layerinformation carriers utilizing light reflection or fluorescence.

The present invention may also be used in ophthalmic applications as acontact lens, a spectacle lens, an intraocular lens, or any other lensused around or inserted into any part of the eye. An obvious example isthe use of the invention for the benefit of short sighted (myopic)people who develop presbyopia, the need for reading glasses as a resultof age-related changes in their natural eye lens. In such anapplication, those people may use a single lens, as a spectacle lens,contact lens, intracorneal lens, phakic intraocular lens or aphakicintraocular lens, or a lens inserted elsewhere in the eye. In thisfashion, they will use one lens for seeing at any distance, near or far.Another obvious utilization of the invention is in an intraocular lens,the artificial lens implanted in the eye after removal of a cataract.Currently, the regular artificial lens has only a single focus and thusthe person into whose eye the lens was implanted has a very limiteddepth of focus and has to use spectacles for most distances of regard.Incorporation of the invention into the implanted lens will afford thepatient focused vision at all distances. Another example of ophthalmicuse is as a replacement of multifocal (progressive) spectacle lenses,which are conventionally designed such that every segment of the lenssurface has a different focus and thus the patient has to move his eyesto focus on objects at different distances. Incorporation of theinvention into a spectacle or contact lens will enable the presbyopicwearer to see objects in focus at all distances through any part of thelens.

In all the applications of the invention, including the examples above,the image from objects at different distances are focused on the retina(or sensor) without appreciable loss of energy, in contradistinction tothe situation in multifocal contact or intraocular lenses.

Considering the ophthalmic applications of the invention, it should benoted that the technique of the invention, when used specifically insuch applications, advantageously enables widening the field of focusand allows clear vision for far distance as well as for near distanceand for the range in between.

The presently existing products for the ophthalmic applications includeglasses, contact lenses, and intraocular lenses (IOLs). The problemsneeded to be solved are in the following. In normal, healthy eyes, eacheye has two refractive areas (lenses). The difference between the lensesis that dioptric strength of one lens is, within short times, constantand its shape does not change. This lens is the cornea. The second lensthat is situated behind the iris is called the “crystal lens” and it isflexible—its dioptric strength is changed by the use of muscles. Whenthe eye lens is relaxed, its bent radius is large and its dioptric poweris relatively small (about 15-16 diopters), which enables a person tosee far-away objects in focus. When a person wants to see close objects,the dioptric strength of the lens needs to be increased (becauseotherwise the picture would be formed behind the retina). The increasein dioptric strength is obtained by contracting the lens; in the processcalled “accommodation”. For a person wanting to refocus from far toclose (up to 30 cm) distances, the lens has to accommodate by 3diopters. The ability to add such dioptric strength will enable a personto see in focus from various distances. Usually, around the age of 40,the flexible lens begins to harden, and the eye muscles become lesseffective, so that it becomes difficult to see close objects. Thisphenomenon is called “presbyopia”. Many of the presbyopic people alsohave a reduced far-vision (myopia or hyperopia). In these and some othercases there arises a need for correcting the focusing ability forvarious distances simultaneously.

Another known problem is astigmatism—the phenomenon associated withvariation of the eye's optical power with change in the direction ofoptical axis. For example one eye may require a correction of onediopter along one axis, while a different correction or no correctionfor another optical axis. The astigmatism typically is due to asymmetryof the cornea or tilting of the crystal lens. When an eye requires twodifferent corrections along two axes with an angle between them being 90degrees, this is called “regular astigmatism”. When the angle is not 90degrees, this is called “irregular astigmatism”. Today, there are sometechniques for correction of regular astigmatism. As for the irregularastigmatism, generally it can be corrected by using a hard contact lenscreating new surface for the eye. However, many (even most) peoplehaving irregular astigmatism have also a cornea condition that does notallow wearing such hard contact lens. The technique of the inventionoffers a novel solution for the problem of both regular and irregularastigmatism.

For correction of presbyopia, particularly for correction of far vision(related to myopia/hyperopia) there exist two typical spectacle-basedcorrection techniques, which though are based on the same idea: the lensis divided into various fields with different focal distances.

In particular, the spectacle can utilize bifocal glasses, i.e. glassesfor focusing at two different distances. The top half of the lens canenable a person to see objects from far and the lower half can enablehim to see objects close up (it is usually used for reading and seeingobjects at a distance of 40 cm). Bifocal glasses though may haveunaesthetic appearance, with a line separating the two halves of eachlens, and also they do not help focusing on middle distance objects,such as TV or computer screen.

The spectacle can also utilize multifocal glasses—two parts of whichlenses are still for far focus (top portion) and for close up (the lowerportion). Between them there is a narrow strip where the top portionchanges slowly to the lower portion. A person can thus see from variousdistances from 40 cm to far away, but only at one object at a time, notclose and far at once. The narrow strip is for seeing middle distanceobjects—so the person has to be ‘skilled’ to wear such glasses. Whileseeing through the narrow strip, person may not turn his eyeball, butrather has to move his/her head and follow the middle distance object tocontinue seeing it in sharp focus. Typically, in these glasses, thevisual field is less than 30 degrees for the reading area, and less than15 degrees for seeing middle distance objects. Thus, in some cases itmay take time for a person to get accustomed to wearing the multifocalspectacles, and in some cases the person never gets used to them.Moreover, manufacturing such glasses is relatively costly.

Correction can also be done with contact lenses. For example, on theperiphery of the lens there may be made a ring with a focal distance fora near field of vision: typically, close up vision is needed forreading, and when reading the eyes usually need to look downwards, thusthe lens will be pushed upwards, and the pupil will use the opticalaccess through the ring. Though, such a solution is not helpful forseeing middle distance objects like a computer screen.

Presbyopia or myopia correction thus can be based on use of bifocal ormultifocal contact lenses, made for example with diffractive orrefractive rings. However in this case double images are typically seen.Also the energetic efficiency is damaged and people have worse vision atlow lighting conditions (e.g. they may not read at such lightingconditions). Yet another technique is to correct one eye for distantobjects, and the other eye for close up objects. This solution resultsin poorer quality, if compared to the case when both eyes see the sameobjects with the same degree of quality. For example this solutionreduces the stereoscopic vision ability.

Turning to IOL lenses, two types of them exist. In the first type, thelens is inserted between the cornea and the iris and it aims at changingthe focal distance of the cornea, while not relying on multifocality.Artisan and Artiflex are examples of products implementing such lenses.They are implanted into eyes of those people whose lenses are normal butrequire refraction correction of the eye. This is the procedure used inlaser eye operations known today.

IOL lenses of the other type are inserted in place of the eye lenses.This procedure is performed when a person's eye lens is removed, e.g.due to cataract. Three most important multifocal types of such IOLsexist today: diffractive lenses, refractive lenses, and accommodativelenses.

The diffractive lenses have two different focal points, whereby one ofthese points is for close up and the other is for far distance. Suchlenses, first, distribute the light energy between the focal points;second enable only partial focusing on middle distance objects, betweenthe two focusing lenses; third are typically sensitive to wavelengths(when and because the lens rings are diffractive). Therefore the personmay see a picture where some colors are in focus while other colors areout of focus. The refractive IOLs also distribute energy between fociand may provide inadequate quality of middle distance vision.

Accommodative lenses are those imitating the natural eye lens: they canmove or can change the length of focus when the eye muscles put pressureon it. Such lenses require a complicated insertion procedure and theirtechnology is yet immature.

Turning now to astigmatism, the regular astigmatism can be corrected byglasses or contact lenses. For making glasses, the angle of astigmatismhas to be determined by an accurate testing. The lens needs to bemanufactured with high precision. For making use of contact lenses, theyneed to remain stable in the eye. Thus a contact lens is used with asmall weight (stabilizer) preventing it from moving around the pupil.Such contact lenses are custom-made according to the angle ofastigmatism, and are costly.

The IOL lenses do not presently provide an accepted solution forastigmatism. Even to the contrary, the IOL insertion procedure may leadto creation of various astigmatic problems. For example, the astigmatismmay be worsened if a surgeon would orient the lens at an angle differentfrom the angle of astigmatism or the aperture through which the lens isinserted would cause curvature of the cornea. Hence, nowadays it iscommon practice that a person with even an astigmatism of one diopter isnot advised to have a IOL multifocal lens implant.

Turning now to the technique of the present invention, it is suitablefor application with glasses, contact lenses and intraocular lenses. Itcan be applied to stretch and broaden the depth of focus for a single-,bi- or multifocal lens. The technique does not need to rely on a certainangle or on eye's ability to focus, and so it can be applied forcorrection of presbyopia, myopia and regular as well as irregularastigmatism.

In particular the technique of the invention can stretch the depth offocus for example making it 3 diopters for pupil size varying betweendiameters of 1.5 mm up to 5 mm.

For the use with contact lenses and IOLs, the phase element positionedclose to the lens or IOL principal plane (or two phase elements atopposite sides of the lens principal plane) may be sufficient to correctsimultaneously all the vision problems mentioned above. The phaseelement may be produced as a surface to which a patterned coating of asimilar refractive index is added. Such fabrication procedure isgenerally less costly than bifocal or multifocal lens fabricationprocedure.

It should be noted that the technique of the present invention allowsfor using the phase affecting element in the following positions in theeye: (1) being attached or incorporated in the eye lens (crystal lens);being located in the anterior chamber (aqueous humour) between the irisand cornea; or being located inside the cornea. In the latter case, theupper, external layer of the cornea is first removed, the phase elementis placed (forming a thin layer of about 10 microns), and the removedlayer is returned back.

For the use with glasses, the phase element may be reproduced on thesurface of the glasses lens, e.g. it may include periodically ornon-periodically replicated phase-transition pattern. With regards tothe non-periodic replication, the replication may be made for examplewith slowly changing period (frequency), so as to generate, by theglasses, a consistent focal point. For example, addition of the elementcan enable the person to see things close-up with the same glasses usedfor far vision. A large, even an entire field of view may be correctedfor both far and near vision. It should be noted that the phaseaffecting element may advantageously be used in sun glasses as well,where the sun glasses either have certain optical power or not.

As indicated above, the lenses can be produced with phase elements onboth sides. This facilitates obtaining uniformly high quality of visionwithin the large or full field of view. In some embodiments, using aphase element including many phase transitions (e.g. replicated phasepattern), the vision quality may be improved if the phase effect of thephase transition is varying. If the phase pattern is realized as aplurality of binary phase transitions, the phase transitions may be ofdifferent height.

The phase element of the invention is not required to have any focalpower if used with a lens (though in some embodiments it is integralwith the lens and therefore not separable). Though, it allows wellfocused and highly resolved all-optical imaging. In digital cameraimaging post processing of obtained image might be performed, but thisis not the case of ophthalmic applications.

As it has been mentioned above, the phase affecting element of theinvention is non-diffractive (has relatively large features andrelatively low spatial frequencies of the features distribution) andconfigured to have a reduced sensitivity to quadratic phase factor,affecting the OTF more when the image is defocused and/or at relativelyhigh spatial frequencies. The quadratic phase factor is relevant onlyfor spatially incoherent light: it as a result of the auto correlationoperation applied to the phase distribution in the aperture plane (as in(4)). Since all typical conditions involve illumination with incoherentlight, the operation of the element of the invention suits theophthalmic applications.

The auto correlation (4) of the spatial phase distribution over theaperture plane can be written as:

$\begin{matrix}{{H\left( {\mu_{x},{\mu_{y};Z_{i}}} \right)} = \frac{\int_{- \infty}^{\infty}{\int_{- \infty}^{\infty}{P\mspace{11mu}\begin{pmatrix}{{x + \frac{\lambda\; Z_{i}\mu_{x}}{2}},} \\{y + \frac{\lambda\; Z_{i}\mu_{y}}{2}}\end{pmatrix}{P^{*}\begin{pmatrix}{{x - \frac{\lambda\; Z_{i}\mu_{x}}{2}},} \\{y - \frac{\lambda\; Z_{i}\mu_{y}}{2}}\end{pmatrix}}\ {\mathbb{d}x}\ {\mathbb{d}y}}}}{\int_{- \infty}^{\infty}{\int_{- \infty}^{\infty}{{{P\left( {x,y} \right)}}^{2}{\mathbb{d}x}{\mathbb{d}y}}}}} & (9)\end{matrix}$

While in focus, P(x,y) is the binary pupil function, which is “1” withinthe pupil, and “0” outside, μ_(x), μ_(x) are the spatial frequencies,Z_(i) is the distance between the imaging lens and the sensor (retina)and x, y are the spatial coordinates in the aperture plane.

When the phase element of the invention is included in the opticalsystem and defocusing is introduced, the generalized pupil function canbe described as:P(x,y)=|P(x,y)|exp[ikW(x,y)]  (10)Here W(x,y) is a quantity proportional to the phase of the wavedistortion; and wave vector k equals 2π/λ.

If the distortion is caused only by defocusing, W(x,y) has the form of:

$\begin{matrix}{{{W\left( {x,y} \right)} = {W_{m}\frac{\left( {x^{2} + y^{2}} \right)}{b^{2}}}},} & (11)\end{matrix}$where b is the radius of the aperture P (similarly to (1)); thecoefficient W_(m) determines the severity of the defocusing (thedeviation from the geometric focusing condition, similarly to (2)).

One of the aspects of the invention is to design a phase only elementhaving large spatial features such that the auto correlation operationof (10) will generate OTF that is invariant over the desired field ofview to quadratic phase distortion created when defocusing, as in (2),is introduced. This condition can be defined mathematically throughvarious criteria, generally requiring the OTF to be as much as possibleaway from zero for a certain region of focus in certain region ofspatial frequencies.

For ophthalmic applications several additional factors need to beconsidered. For example the spectacles are typically about 1.5-2 cm (ormore than that) away from the aperture plane of the lens of the eye. Aperson needs to change his/her line of sight. The diameter of the eyepupil of a person depends on illumination conditions and varies in therange 2-4 mm. In preferred case, the spectacles and contact lenses donot require very precise positioning or orienting.

Hence, the spectacles need to generate the effect of the phase elementfor a wide field of view and not for a certain line of sight. This isalso true for contact lenses and IOLs, but these can move more or lesstogether with the eye ball and its varying line of sight, so thecondition may be relaxed.

The inventors have found that the above ophthalmic-related goals can beat least partially fulfilled by spatial replicating of a basic phasepattern structure. For example, a better performance has been achievedwith a periodic phase pattern structure on both sides of the glass ofthe spectacles.

The inventors have conducted experiments proving the applicability ofthe technique of the invention in the ophthalmology. In particular, theinventors have fabricated a phase element (and an experimental opticalsystem) that provided extended depth of focus within 3 Diopters, for eyepupil diameter varying in the range of 2-4 mm and with high tolerance tothe exact position of the element relative to the pupil of the eye lens.Thus, several embodiments provided correction for presbyopia, since the3 Diopters improvement significantly improved the quality of near visionwhile substantially not affecting the high quality of far vision. Itshould be understood, that the obtained 3 Diopters range of improvementis similar to accommodation in that the element itself does notdistribute energy between foci and is generally non-diffractive. Infact, when the phase element is positioned in front of the eye itprovides the depth of focus within the range of 0-3 Diopters. If theelement is added to a lens of for example 2 Diopters optical power, theoperation range is 2-5 Diopters.

FIGS. 11A and 11B present two images of a typical visual acuityresolution target, respectively, obtained by the technique of theinvention and by an optical system with presbyopia with 1.75 Diopters.The imaging optical system was built with optical parameters equal tothose of the human eye, in accordance with the publication L. A.Carvalho, “A simple mathematical model for simulation of the humanoptical system based on in vivo corneal data,” Revista Brasileira deEngenharia Biomedica, 19, 29-37 (2003). One may see that indeedimprovement of 1.75 Diopters is significant (each line in the resolutiontarget is equivalent to 0.25 Diopters). The pupil diameter used in thisexperiment was 2.5 mm while the phase element was positioned 17 mm awayfrom the pupil.

Here are some definitions of the parameters used to test and quantifythe ophthalmic performance. Visual acuity (VA) is defined as theresolving power of the eyes' optical system, or the ability to see twoseparate objects as separated. Snellen acuity chart includes lettersthat are constructed so that the width of a stroke equals the width of agap. In most Snellen charts, letters are 5 units high and 4 units wide.Visual acuity is specified in terms of the angular size of the gap forthe smallest sized letter the patient can identify. “Normal” VA isspecified as the ability to detect a gap subtending 1 minute of arc. Forany target distance, the linear width of the gap χ, for any givenangular sub tense, may be determined as follows:

${{\tan\;\theta} = \frac{\chi}{R}},$where R is the distance to the target in meters. For a gap subtending 1minute of arc, and distance of R=6 m one obtains:χ=6 m·tan θ=6 m·0.000291=0.001746 m=1.746 mm

For the Snellen fraction (SF) the definition is:

${{SF} = \frac{R_{T}}{R_{5}}},$where R_(T) is the testing distance and R_(S) is the distance at whichthe smallest letter read subtends at angle of 5′ of arc.

The 6/6 acuity standard can be described as a minimum angle ofresolution (MAR) of 1 min arc. Log MAR is the logarithm at base 10 ofthe MAR in min arc at a viewing distance of 6 m. In this system eachstep is 0.1 log units. The 0.1 ‘credit’ for reading full row of 5letters can be subdivided into 5×0.02 steps for reading each individualletter.

The contrast sensitivity (CS) is defined as:

${C = \frac{L_{\max} - L_{\min}}{L_{\max} + L_{\min}}},$where C is the contrast. It is computed for sine wave gratings while thespatial frequency is plotted along the x axis and the CS is plottedalong the y axis.

In this way the invention was also tested on a group of persons. FIGS.12A and 12B present the obtained results (visual acuity diagrams) fortwo phase elements, numbered 31 and 32. The shown improvement in visualacuity (VA, on the diagrams' vertical axes) relates to the improvementin Diopters (D), resulted from the increased depth of focus due to thephase element:D=2.5·VA  (12)

Elements 31 and 32 had annular like structure with external diameter of2.6 mm for the ring replicated with basic period of about 3.5 mm andetched depth of 350 nm (equivalent to generated phase difference ofabout π/2). The elements were fabricated on both sides of a flat glassof 2 mm width. The number of replicates was either 4 or 5. Thedifference between elements 31 and 32 was in slight change in thediameter of the basic pattern and in its etching depth.

All of the tested persons were examined by an optometrist and had far VAof 6/6 or better. None of them had deficit in color vision or contrastsensitivity. All of the persons had presbyopia and needed opticalcorrection for near distance. VA tests were made with logarithmiccharts, Precision Vision chart for testing at 40 cm and Early TreatmentDiabetic Retinopathy Study (ETDRS) for testing at distance. The groupincluded 5 persons at age range from 49 to 65 with an average of 55±3.4.The persons were tested at three different luminance conditions (100,40, and 25 Watts of the illuminating lamp) which affected the pupilsize: the high luminance led to the pupil sizes of 1.5 to 2.5 mm, themedium luminance to the pupil sizes of 2.5 to 3.5 mm, and the lowluminance to the pupil size of 3 to 4 mm.

It can be seen from FIGS. 12A and 12B that the achieved improvement inVA was substantial for the three luminance conditions.

For example, the phase element 31 has improved the near distance VA forthe high, middle and low luminance to 0.096±0.048, 0.95±0.014 and0.115±0.048 in Log units respectively (these visual acuities are shownas lower and lighter portions of the vertical bars). The improvement inthe visual acuity is the difference between the upper (darker) portionsof the bars and the lower (lighter) portions of the bars, e.g. 0.34(0.44−0.1) for element 31 at illumination power of 100 W. In both FIGS.12A and 12B the standard deviation is designated as a line plotted ontop of the bar presented for each measurement.

The persons of the test group were asked to read. Table 1 presents theresults obtained with invented elements 51 and 52 All the tests weretaken with the high luminance only.

TABLE 1 Summary of the reading test. VA with distance VA with correctiondistance (ETDRS Log correction Im- EDOF units Jaeger and EDOF prove-element and Snelen) lens ment No Refraction ge 0.6 0.1 0.5 52 & 51Myopic −5.00 − 56 J8 J1 1.25 × 76 6/24 6/7.5 0.62 0.2 0.42 52 & 51Myopic −2.75 53 J8− J4 6/24− 6/9.5 0.54 0.12 0.42 51 Myopic −0.5 − 65J6− J1 100 × 80 6/19− 6/7.5 0.54 0.12 0.42 51 Hyperopic 52 J6− J1 Plan6/19− 6/7.5

Elements 31, 32, 33, and 35 were tested for far distance vision as well:the results of the distance vision tests are summarized in Table 2. Theresults show small deficit, less than 0.1 Log units, in VA for most ofthe persons. Different rows correspond to different persons.

TABLE 2 Summary of the effect of the invented element on far vision.Corrected Element Element Element Element Visual Acuity No. 35 No. 33No. 32 No. 31 for Distance −0.06 −0.1 −0.1 0.08 −0.08 0.22 0.2 0.16 0.260 0.08 0.18 −0.12 0.26 −0.06 0 0.06 0.04 0.24 0.06 −0.02 −0.02 0.04−0.02 0.04 0.44 0.064 0.004 0.164 −0.008 0.055 −0.064 0.057 0.06 0.03

Additional tests that were performed over the test group included:

-   -   5 persons were tested monocularly with the “Ichihara” color        test, no reduce in performance was found for any of them.        Therefore the element preserves color integrity;    -   Contrast sensitivity test with Sine Wave Contrast Test (SWCT) of        Stereo Optical Co. Inc. was taken with 5 persons, all showed no        reduce in performance or reduce corresponding to their results        for the near vision optical correction;    -   Three dimensional capabilities and stereoscopy were tested. No        reduction in stereoscopic capabilities was observed.

It should be understood that the presented approach, although itsperformance was quantified only for near and far vision, producesaxially continuous focused vision (i.e. continuously extended depth offocus).

FIG. 13 presents similar results (the improvement in the visual acuity)obtained for elements 51, 52 and 53 when tested with the same testgroup. The results in Jaeger units appear in the right part of the plot.This group of elements is similar to elements 31, 32, 33, 35: thedifference is in the size of phase pattern period and the etching depth(the variation was few percentages in comparison to the valuespreviously specified for elements 31, 32, 33 and 35).

As it has been mentioned above, a large portion of population,especially of the bifocal population, has regular or even irregularastigmatism which means that their eye has different focal lengths alongdifferent spatial axes. The technique of the present invention uses thephase element providing an extended depth of focus for achieving highimaging quality for both cases of astigmatism. The presented solutionwas experimentally tested with an optical setup modeling the human eye.

To this end, the invented annular phase element has been used with largespatial features configured for being relatively insensitive toquadratic phase of defocusing under the condition of spatiallyincoherent illumination. The element can be used with spectacles as wellas with contact lenses or IOLs.

The optical element was positioned 17 mm away from the imaging lens thatmodeled the human eye. Astigmatism was inserted into that lens (eitherregular or irregular. The phase element was an annular like structurewith external diameter of 2.6 mm for the ring (as described above),replicated with basic period of about 3.5 mm. The etching depth was ofabout 350 nm and provided a phase difference of about π/2 for thoseoptical paths passing through the pattern compared to the optical pathsnot passing through the pattern. The phase pattern was fabricated onboth sides of flat glass having width of 2 mm. The fabrication on bothsides provided some improvement in performance. Some other elements hadthe phase transition of other values, such as π, 1.5π. Generally, thevalues of the phase effects differ by not more than 16π, 8π, 4π, 2π,dependent on embodiment. Likewise, a lower bound for an average width ofthe phase transition can be set for example to 5λ, 25λ, 150λ, or 250λ.The larger this characteristic width, the higher the energeticefficiency and the lesser chromatic aberration of the phase-affectingelement.

FIGS. 14A and 14B present the obtained experimental results forirregular astigmatism. FIG. 14A is obtained with the phase element andFIG. 14B is obtained without it. Likewise, FIGS. 15A and 15B present theobtained experimental results for regular astigmatism: FIG. 15A wasobtained with the phase element and FIG. 15B was captured without it. Inboth cases of regular and irregular astigmatism one may see asignificant improvement that was obtained. This improvement can beestimated to be equivalent to 1.5-2 Diopters (each line of improvementin the ophthalmic resolution chart is 0.25 Diopters).

The technique of the invention can also be used for treatment of myopianpeople, especially for children. Using glasses is not recommended formyopian children, because it may cause progressing (worsening) of theirmyopia. With the extended depth of focus treatment eyes do not need toaccommodate (since the element extends the focus rather than refocusesthe eye), therefore the progress of the myopia can be stopped ordelayed. It should be noted that the phase elements may include acombination of local phase patterns arranged in a spaced-apartrelationship along two axes, though distributed with a certain degree ofrandomality. For example similar patterns replicated at variousrelatively random positions may also be used. Generally, thephase-affecting element may include various geometrical shapes.

Also, as mentioned above the phase affecting element may be formed bynon-periodic pattern replication. In this connection, the followingshould be noted: randomizing the positions of the replicates may provideon average to have more uniform performance over the large field ofview. This can be obtained since the replicates are non uniformly spreadalong the field of view and thus on average for each angle there is aprobability of obtaining proper pattern of the phase transitions. Inperiodic replications, there can be certain angles for which no properphase-transition appears. On average, in some cases, a more functionalor more optimized device can be obtained with non-periodic (e.g. theslightly non-periodic, for example with increasing or decreasing period)or random replication. Also, the use of non-periodic replication canease the brain adaptation to the phase element since fluctuations inquality of vision can be lower. Therefore the adaptation time requiredby the brain can be shorter for such a structure. Moreover, thefabrication of such an element with randomly located replicates might besimpler, since no tolerances are required regarding the period ofreplication. A phase element with randomly located replicates might havebetter performance for varying illumination conditions because theperiod does not have to be adapted to the pupil size of the eye.

Those skilled in the art will readily appreciate that variousmodifications and changes can be applied to the embodiments of theinvention described hereinbefore without departing from its scopedefined in and by the appended claims.

1. An imaging arrangement comprising: an imaging lens assembly includingat least one lens having a certain affective aperture, and at least oneoptical element associated with said at least one lens and configured toprovide an extended depth of focus of the imaging arrangement, saidoptical element being configured as a phase-affecting, non-diffractiveoptical element defining a spatially low frequency phase transition,said optical element together with its associated lens defining apredetermined pattern formed by spaced-apart optically transparentfeatures of different optical properties, position of at least one phasetransition region of the optical element within the lens plane beingdetermined by at least a dimension of said affective aperture.
 2. Thearrangement of claim 1, wherein said lens assembly includes the singlelens associated with the single optical element.
 3. The arrangement ofclaim 1, comprising the lens assembly including an array of lenses, andan array of the optical elements, each optical element being associatedwith the corresponding one of the lenses.
 4. The arrangement of claim 1,wherein said optical element is configured as a phase-only element. 5.The arrangement of claim 4, wherein said optical element is configuredas a binary mask.
 6. The arrangement of claim 1, wherein said opticalelement is a configured as a phase and amplitude affecting element. 7.The arrangement of claim 1, wherein the optical element is configured tomaximize a defocused optical transfer function (OTF) of the imagingarrangement by providing the out of focus OTF as much as possible awayfrom zero.
 8. The arrangement of claim 7, wherein the optical element isconfigured to produce proper phase interference relation between lightportions passing through different regions of the imaging arrangementcorresponding to the different features of the pattern to thereby reducea quadratic phase factor resulting from light getting out of focus ofthe imaging lens.
 9. The arrangement of claim 1, wherein said at leastone transition region is configured as a pi-phase transition for acertain wavelength for which the optical element is designed.
 10. Thearrangement of claim 1, wherein said at least one transition region isconfigured as about pi/2 phase transition for a certain wavelength rangefor which the optical element is designed.
 11. The arrangement of claim1, wherein the position of said at least one transition region withrespect to the imaging lens is determined by optical power of theimaging lens.
 12. The arrangement of claim 7, wherein the position for Ntransition regions of the optical element within the imaging lens planemaximizing the OTF is determined as:$\max\limits_{a_{n}}\left\{ {\min\left\{ {\left\lbrack {{\overset{\sim}{D}(v)}{\sum\limits_{n = 1}^{N}\;{a_{n}{{rect}\left( \frac{v - {n\;\Delta\; v}}{\Delta\; v} \right)}}}} \right\rbrack \otimes \left\lbrack {{\overset{\sim}{D}(v)}{\sum\limits_{n = 1}^{N}\;{a_{n}{{rect}\left( \frac{v - {n\;\Delta\; v}}{\Delta\; v} \right)}}}} \right\rbrack} \right\}} \right\}$values for a_(n) providing maximum for minima of an expression for autocorrelation of a Coherent Transfer Function (CTF) of the imaging lens,where a_(n) equals either 1 or −1, {tilde over (D)}(v) being the CTF ofthe imaging lens corresponding to out of focus position of an objectbeing imaged and being determined as${{\overset{\sim}{D}(v)} = {\exp\left( \frac{{\mathbb{i}}\; 4\Psi\; v^{2\;}}{D^{2}} \right)}},$wherein D is the affective aperture dimension, v is a coordinate of theaffective aperture in the CTF plane, and ψ is a phase factorrepresenting a degree of getting out of focus.
 13. The arrangement ofclaim 1, wherein said at least one transition region has a sub-patternformed by an array of variable phase transition sub-regions.
 14. Thearrangement of claim 9, wherein said at least one pi-phase transitionregion has a sub-pattern formed by an array of variable pi-phasetransition sub-regions.
 15. The arrangement of claim 1, wherein theoptical element is configured as at least one annular transition region.16. The arrangement of claim 1, wherein the optical element isconfigured as a grid.
 17. The arrangement of claim 1, wherein saidoptical element is spaced-apart from the imaging lens along an opticalaxis of the imaging lens.
 18. The arrangement of claim 1, wherein saidoptical element is attached to the imaging lens.
 19. The arrangement ofclaim 1, wherein said optical element is made integral with the imaginglens.
 20. The arrangement of claim 1, wherein said optical element isconfigured as a mask formed by an array of said transition regionsarranged in a spaced-apart relationship being spaced by the opticallytransparent regions of the imaging lens within the imaging lens plane.21. The arrangement of claim 1, comprising two phase affecting opticalelements located in spaced-apart substantially parallel planes atopposite sides, respectively, of said at least one lens.
 22. Thearrangement of claim 19, wherein said at least one transition region isformed as a surface relief on the imaging lens surface, defining a lensthickness within said at least one region different from that withinother regions of the lens.
 23. The arrangement of claim 19, wherein saidat least one transition region is formed by a material having refractiveindex different from that of the imaging lens material.
 24. Thearrangement of claim 19, wherein said optical element is configured as amask formed by an array of the phase transition regions formed by amaterial having refractive index different from that of the imaging lensmaterial.
 25. The arrangement of claim 7, wherein the optical element isconfigured to maximize the OTF by reducing high-frequency cancellationat large shifts of a Coherent Transfer Function (CTF) of the imaginglens.
 26. The arrangement of claim 7, wherein the optical element isconfigured to maximize the OTF by reducing sensitivity of the lensarrangement to shifts of a Coherent Transfer Function (CTF) of theimaging lens while getting out of focus.
 27. The arrangement of claim 1,wherein the optical element is configured to produce periodicreplication of a lateral phase shape of a light field propagatingthrough the imaging lens.
 28. The arrangement of claim 1, wherein theoptical element is configured in accordance with a free spacepropagation of the optical element function for a distance between theoptical element and the imaging lens plane.
 29. The arrangement of claim1, wherein the optical element is configured to produce non-periodicreplication of a lateral phase shape of a light field propagatingthrough the imaging lens.
 30. The arrangement of claim 1, wherein theoptical element is configured to produce random replication of a lateralphase shape of a light field propagating through the imaging lens. 31.The arrangement of claim 1, for use in patients' spectacles.
 32. Anoptical element for use with an imaging lens in the imaging arrangementof claim 1 for extending depth of focus of imaging, the optical elementbeing configured as a phase-affecting, non-diffractive optical elementdefining a predetermined pattern of spatially low frequency phasetransitions, said pattern being defined by an affective aperture of thegiven imaging lens.
 33. A system for creating an image of an object on adetector plane, the system comprising the imaging lens arrangement ofclaim
 1. 34. The system of claim 32, wherein said object is a screen ofa display device to be imaged on the eye retina constituting thedetector plane.
 35. A display device carrying the imaging arrangement ofclaim
 1. 36. A method for providing a certain extended depth of focus ofan imaging system, the method comprising applying an aperture coding toan imaging lens having a certain effective aperture, by applying to theimaging lens at least one phase-affecting non-diffractive opticalelement configured to define a spatially low frequency phase transitionarrangement and thereby provide a predetermined pattern of spaced-apartsubstantially optically transparent features of different opticalproperties within the imaging lens plane, thereby producing phaseinterference relation between light portions passing through differentregions of the lens arrangement corresponding to the different featuresof the pattern so as to reduce a quadratic phase factor resulting fromlight getting out of focus of the imaging lens and maximize a defocusedoptical transfer function (OTF) of the imaging lens arrangement.
 37. Amethod for designing the optical element of claim 32, said designingcomprising selecting N positions for the phase transitions within theimaging lens effective aperture as those providing maximal contrast ofan Optical Transfer Function (OTF) of the imaging system under a set ofout of focus locations, thereby providing the out of focus OTF as muchas possible away from zero.
 38. The method of claim 37, wherein thepositions for said N transition regions of the optical element withinthe imaging lens plane maximizing the OTF are determined as:$\max\limits_{a_{n}}\left\{ {\min\left\{ {\left\lbrack {{\overset{\sim}{D}(v)}{\sum\limits_{n = 1}^{N}\;{a_{n}{{rect}\left( \frac{v - {n\;\Delta\; v}}{\Delta\; v} \right)}}}} \right\rbrack \otimes \left\lbrack {{\overset{\sim}{D}(v)}{\sum\limits_{n = 1}^{N}\;{a_{n}{{rect}\left( \frac{v - {n\;\Delta\; v}}{\Delta\; v} \right)}}}} \right\rbrack} \right\}} \right\}$values for a_(n) providing maximum for minima of an expression for autocorrelation of a Coherent Transfer Function (CTF) of the imaging lens,where a_(n) equals either 1 or −1, {tilde over (D)}(v) being the CTF ofthe imaging lens corresponding to out of focus position of an objectbeing imaged and being determined as${{\overset{\sim}{D}(v)} = {\exp\left( \frac{{\mathbb{i}}\; 4\Psi\; v^{2\;}}{D^{2}} \right)}},$wherein D is the affective aperture dimension, v is a coordinate of theaffective aperture in the CTF plane, and, and ψ is a phase factorrepresenting a degree of getting out of focus.
 39. The method of claim37, comprising fabricating a mask formed by an arrangement of the Ntransitions spaced-apart from each other in accordance with saidselected N positions.
 40. The method of claim 39, comprising attachingsaid mask to the surface of the imaging lens aperture.
 41. The method ofclaim 37, comprising patterning the surface of the imaging lens apertureto form a mask of the N transitions spaced-apart from each other inaccordance with said selected N positions.
 42. The method of claim 40,comprising providing said surface substantially flat to thereby allowinsertion of the patterned imaging lens into a patient's eye.
 43. Themethod of claim 37, wherein the designing of the optical elementcomprises producing a phase interference relation between light portionspassing through said N regions and spaces between them to thereby reducea quadratic phase factor resulting from light getting out of focus ofthe imaging lens and maximize a defocused optical transfer function(OTF) of an arrangement formed by the imaging lens and the opticalelement.
 44. The method of claim 41, wherein said patterning comprisesapplying material removal to the lens regions within said N positions,and filling said regions, from which the lens material has been removed,by a material of a refraction index different from that of the lens, soas to provide a refraction index difference such that the outer regionof the patterned lens is flat and proper equalization between thedifferent material regions is provided to produce a phase interferencerelation between light portions passing through different materialregions to thereby reduce a quadratic phase factor resulting from lightgetting out of focus of the imaging lens and maximize a defocusedoptical transfer function (OTF) of the patterned imaging lens.
 45. Themethod of claim 41, wherein said patterning comprises applying diffusionor photo polymerization to the lens regions within said N positions, soas to provide a refraction index difference between said N regions andspaces between them such that the outer region of the patterned lens isflat and proper equalization between the different material regions isprovided to produce a phase interference relation between light portionspassing through different material regions to thereby reduce a quadraticphase factor resulting from light getting out of focus of the imaginglens and maximize a defocused optical transfer function (OTF) of thepatterned imaging lens.
 46. The method of claim 37, comprisingimplanting in the patient's eye tissue, within said selected Npositions, an artificial tissue having a refraction index different fromthat of the eye tissue.